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homological algebra

   Also found in: Wikipedia 0.01 sec.
homological algebra [¦hä·mə¦läj·ə·kəl ′al·jə·brə]
(mathematics)
The study of the structure of modules, particularly by means of exact sequences; it has application to the study of a topological space via its homology groups.


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An emphasis on homological algebra allows basic notions on complexes to be presented as soon as modules have been introduced, and an extensive last chapter on homological algebra can form the basis for a follow-up introductory course on the subject.
87 QA612 Based on a June 2005 summer school, this series of 24 lectures introduces the algebraic sets, sheaf theory, and homological algebra leading to the definition and alternative characterizations of local cohomology.
Other topics include topological homological algebra, topological algebraic geometry, sheaf theory, and L-theory.
 
 
 
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